Flat-floor bubbles, dark solitons, and vortices stabilized by inhomogeneous nonlinear media

TL;DR

This paper explores stable flat-floor bubbles, dark solitons, and vortices in inhomogeneous nonlinear media, revealing their stability properties and dynamic behaviors in 1D and 2D settings.

Contribution

It introduces and analyzes the existence and stability of delocalized bubbles and dark modes in media with inhomogeneous nonlinearity, extending prior work on localized solitons.

Findings

1D and 2D bubbles are fully stable.

Vortices with m=1 are stable, m=2 have limited stability.

Unstable dark solitons and vortices exhibit characteristic decay behaviors.

Abstract

We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of flat-floor \textquotedblleft bubbles", and topological excitations, in the form of dark solitons in 1D and vortices with winding number $m$ in 2D. Unlike bright solitons, delocalized bubbles and dark modes were not previously considered in this setting. The ground and excited states are accurately approximated by the Thomas-Fermi expressions. The 1D and 2D bubbles, as well as vortices with $m=1$, are completely stable, while the dark solitons and vortices with $m=2$ have nontrivial stability boundaries in their existence areas. Unstable dark solitons are expelled to the periphery, while unstable double vortices split in rotating pairs of unitary ones. Displaced stable vortices precess around the central point.